{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(2,1)\n",
    "plt.subplot(2,1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "x=np.linspace(-10,10,100)\n",
    "y=np.sin(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_13243/3424952855.py:2: MatplotlibDeprecationWarning: Auto-removal of overlapping axes is deprecated since 3.6 and will be removed two minor releases later; explicitly call ax.remove() as needed.\n",
      "  plt.subplot(2,1,2)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fc022c16590>,\n",
       " <matplotlib.lines.Line2D at 0x7fc022c16560>,\n",
       " <matplotlib.lines.Line2D at 0x7fc022c164d0>,\n",
       " <matplotlib.lines.Line2D at 0x7fc022c16410>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x,y, marker='o')\n",
    "plt.subplot(2,1,2)\n",
    "a = np.arange(10)\n",
    "plt.plot(a, a * 1.5, a, a*2.5, a, a* 3.5, a, a*4.5)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.10.6 64-bit ('3.10.6')",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.6"
  },
  "orig_nbformat": 4,
  "vscode": {
   "interpreter": {
    "hash": "d44d76ef8cbbc4331cecfe2e59228ac31ebb71026289858a116838be7168b60b"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
